To obtain a random sample of lamps to inspect, the selection process should ensure that every lamp has an equal chance of being chosen. Let's evaluate the options:
A) 400 lamps on the first 10 floors - This method is not random, as it only samples from the first 10 floors, potentially excluding lamps from other floors.
B) All lamps in booked rooms - This method is not random because it focuses only on booked rooms, which may not represent the entire population of lamps in the hotel.
C) 100 lamps on each floor chosen randomly - This option provides a random sample because it ensures that lamps from all floors are considered, and the selection is random within each floor.
D) All lamps from the rooms with king-sized beds - This method is not random as it only samples from rooms with king-sized beds, again potentially excluding many lamps in other rooms.
Based on the criteria for a random sample, the best choice is:
C) 100 lamps on each floor chosen randomly.